When we estimate distances from velocity data it is sometimes necessary to use times to t t2 t3 that are not equally spaced We can still estimate distances using the time periods Ati ti ti 1 For example a space shuttle was launched on a mission the purpose of which was to install a new motor in a satellite The table provided gives the velocity data for the shut etween liftoff and the jettisoning of the solid rocket boosters Use these data to estimate the height h above Earth s surface of the space shuttle 62 seconds after liftoff Give the upper approximation available from the data 48623 X ft Event Launch Begin roll maneuver End roll maneuver Throttle to 89 Throttle to 67 Throttle to 104 Maximum dynamic pressure Solid rocket booster separation Time s Velocity ft s 0 10 15 20 32 59 62 125 0 180 319 442 742 1100 1430 4052